The V-filtration for tame unit $F$-crystals

Details The V-filtration for tame unit $F$-crystals The V-filtration for tame unit $F$-crystals

2011-10-14

arxiv.org/abs/1110.3269v2

Mathematics

Algebraic Geometry

Comments welcome; v2 fixes minor typesetting errors

Scientific paper

Let X be a smooth variety over an algebraically closed field of characteristic p > 0, Z a smooth divisor, and j : U = X\Z --> X the natural inclusion. An axiomatizing of the properties of a V -filtration on a unit F-crystal is proposed and is proven to determine a unique filtration. It is shown that if M is a tame unit F-crystal on U then such a V -filtration along Z exists on j_*M. The degree zero component of the associated graded module is proven to be the (unipotent) nearby cycles functor of Grothendieck and Deligne under the Emerton-Kisin Riemann-Hilbert correspondence. A few applications to A^1 and gluing are then discussed.

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